Preprint

Inserted: 12 oct 2023
Last Updated: 26 feb 2024

Year: 2023

Abstract:

We prove the general version of point-to-point constructive controllability results for control affine systems on compact manifolds with drift under nonholonomic constraints on controls. Namely, we find the sufficient (and almost necessary) conditions when arbitrarily small controls satisfying such constraints can be found to steer the ODE from one given state to another. This result provides controllability for systems having invariant measures supported on the whole phase space and being finite (for example, for divergence-free drifts) or, more generally, for nonwandering flows.

Keywords: controllability, nonholonomic control, Chow-Rachevsky theorem, control affine system, systems with drift

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• ControlNonholonomCompact24a.pdf